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We evaluate the corrections to the matching coefficient of the vector currentbetween Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) tothree-loop order containing a closed heavy-fermion loop. The result constitutesa building block both for the bottom- and top-quark system at threshold. Strongemphasis is put on our completely automated approach of the calculationincluding the generation of the Feynman diagrams, the identification of thetopologies, the reduction to master integrals and the automated numericalcomputation of the latter.

Completely automated computation of the heavy-fermion corrections to the three-loop matching coefficient of the vector current